On the lead you have one sure trick in spades, two clubs and two hearts.  If the diamond finesse is good there are four
 tricks in the suit to make the nine tricks required.  That assumes you can take the finesse a sufficient number of times.
There are only two entries to dummy though, and three entries may be required.  In this case that is the problem.  
See what happens when you drop you spade king under the ace.  Now the jack or ten provides the third entry and the 
diamond king is caught.
                                 Quite simple really.   No-one sent in a solution which I find hard to believe.